5(7x-5)(4x+5)=0

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Solution for 5(7x-5)(4x+5)=0 equation: 


Simplifying
5(7x + -5)(4x + 5) = 0

Reorder the terms:
5(-5 + 7x)(4x + 5) = 0

Reorder the terms:
5(-5 + 7x)(5 + 4x) = 0

Multiply (-5 + 7x) * (5 + 4x)
5(-5(5 + 4x) + 7x * (5 + 4x)) = 0
5((5 * -5 + 4x * -5) + 7x * (5 + 4x)) = 0
5((-25 + -20x) + 7x * (5 + 4x)) = 0
5(-25 + -20x + (5 * 7x + 4x * 7x)) = 0
5(-25 + -20x + (35x + 28x2)) = 0

Combine like terms: -20x + 35x = 15x
5(-25 + 15x + 28x2) = 0
(-25 * 5 + 15x * 5 + 28x2 * 5) = 0
(-125 + 75x + 140x2) = 0

Solving
-125 + 75x + 140x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-25 + 15x + 28x2) = 0

Factor a trinomial.
5((-5 + -4x)(5 + -7x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve:

Simplifying
-5 + -4x = 0

Solving
-5 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -4x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4x = 0 + 5
-4x = 0 + 5

Combine like terms: 0 + 5 = 5
-4x = 5

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25

Subproblem 2
Set the factor '(5 + -7x)' equal to zero and attempt to solve:

Simplifying
5 + -7x = 0

Solving
5 + -7x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -7x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7x = 0 + -5
-7x = 0 + -5

Combine like terms: 0 + -5 = -5
-7x = -5

Divide each side by '-7'.
x = 0.7142857143

Simplifying
x = 0.7142857143
Solution
x = {-1.25, 0.7142857143}

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